code: def _log_ndtr_asymptotic_series(x, series_order):
      """Calculates the asymptotic series used in log_ndtr."""
      npdt = dtype_util.as_numpy_dtype(x.dtype)
      if series_order <= 0:
          return npdt(1)
      x_2 = tf.square(x)
      even_sum = tf.zeros_like(x)
      odd_sum = tf.zeros_like(x)
      x_2n = x_2  # Start with x^{2*1} = x^{2*n} with n = 1.
      for n in range(1, series_order + 1):
          y = npdt(_double_factorial(2 * n - 1)) / x_2n
          if n % 2:
              odd_sum += y
          else:
              even_sum += y
          x_2n *= x_2
      return 1.0 + even_sum - odd_sum
  
file_path: probability/tensorflow_probability/python/internal/special_math.py
imports: import numpy
  import tensorflow.compat.v2
  from tensorflow_probability.python.internal import dtype_util
label_desc: Use image node_id 5 for calling a global function with example usage: _log_ndtr_asymptotic_series(x, series_order) and returns: unknown, npdt